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Sparkle is one of the many firms in the market for toothpaste, which is in long-run equilibrium.a. Draw a diagram showing Sparkle's demand curve, marginal-revenue curve, average-total-cost curve, and marginal-cost curve. Label Sparkle's profit-maximizing output and price.b. What is Sparkle's profit? Explain.c. On your diagram, show the consumer surplus derived from the purchase of Sparkle toothpaste. Also show the deadweight loss relative to the efficient level of output.d. If the government forced Sparkle to produce the efficient level of output, what would happen to the firm? What would happen to Sparkle's customers?
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So if you look in the text figure for shows us exactly what we're looking for in part A, we have a monopolistic lee competitive firm. There's the demand, marginal revenue, marginal cost and average total cost curves. So everything there is what we need. All we need to do is just reproduce that diagram exactly as it is. So this is going to show the market for sparkles toothpaste. Okay, the first thing we need to find here is the profit maximizing output and price. Well, we know firms always want to produce your marginal revenue equals marginal cost. So that's here. Quantity produced. Normally marginal revenue equals demand. But for the monopolistic Lee competitive firm, that's not the case. Instead, demand is greater than marginal revenue. So instead of the price being marginal cost here instead the prices here at P, the difference between those two being the markup. Okay, Now what is sparkles, profit sparkles. Profit is going to be that mark up times the quantity produced. In other words, their profit is equal to the markup on each unit times all of the units that are sold. Okay, Now we need to show the consumer surplus that we actually get from purchasing sparkle toothpaste. Okay, so let's zoom in real quick Just to make this a little clear. Consumer surplus is always bounded at the bottom by price, and bounded on the right by the demand curve will just extend the demand curve all the way to the vertical axis, and it's bounded on the left by the vertical axis. So that green triangle there is going to be the consumer shirt plus. All right now, we also need to find the dead weight loss. And in this case, it's the dead weight loss of the fact that we have a monopolistic Lee competitive firm as opposed to it perfectly competitive firm. So recall that for the perfectly competitive firm, marginal revenue equals demand. Right? We can see that right here, but that's not the case here. And that is where the dead weight loss comes from. So everywhere the marginal revenue is less than demand causes a dead weight loss, and it's gonna be this triangle here, so it's bounded on the left. By the quantity produced, it's bounded on the bottom by the marginal cost curve and bounded on the top by the demand curve. That's our dead weight loss. Okay, so we have both of those now for part D. If the government forced sparkle to produce the efficient level of output, what would happen to the firm? Well, it's profits right here. Would go to zero. Why? Because the markup would be zero and zero times. Any quantity is gonna equal zero. Okay, so with that in mind again, go back to the perfectly competitive firm. What? Our profits. Profits are equal to zero again. We're talking about economic profits, not accounting profits. Right. But profits are equal to zero. So if this monopolistic Lee competitive firm was forced to act like they were a competitive firm, what would happen to the level of output? The level of output would increase, as we can see right here, excess capacity would go to zero because the quantity produced would become the efficient scale quantity. Okay, what would happen to sparkles customers? Well, you would see the consumer shirt plus this green triangle here increase because, remember, what is the consumer surplus founded on at the bottom of the price? And as the price falls, that triangle increases. And that signifies that the consumer surplus is also increasing
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